The Angular Overlap Method

Relative energies of the metal d-orbitals and ligand orbitals using the AOM in an octahedral coordination compound, where the ligands act solely as c7-donors. 

Lastly, we consider the case of ligands that can act as both tr-donors and r-donors. In this case, the ar-interacting ligand orbitals will lie lower in energy than the metal s d-orbitals, so the ligand orbitals will be stabilized by e and the (T-interacting d and AOs will be destabilized by 3e, as shown in 

In the square planar geometry (not shown), the AOM has an additional parameter e jj which extends the theory to include the overlap of mixing of the (n — I )d AO and the ns AO. This has the effect of decreasing the energy of the d orbital in a square planar LF so that its energy is given by e, — 4ejj. 

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A simplification of this method is that put forward by Jergensen et al. and called the "angular overlap method (2, 6). This method has the advantages of simplicity and of the transferability of the parameters from one chromophore MXq to another MXp of different symmetry if all the M-X distances are the same. 

The application of the angular overlap method to MXg chromophores of trigonal bipyramidal and square p3u-amidal stereochemistry leads to the patterns of Fig. 2 for the energies of the antibonding "d molecular orbitals (dc). The crystal field model leads to a similar pattern. 

In addition, these diagrams of homoleptic complexes (with all the ligands identical) are simpler than those of heteroleptic complexes with variation within the Ugand set. The angular overlap method (Section 10.4) provides a strategy for predicting electronic structure information for heteroleptic complexes. 

More sophisticated results were obtained by the angular-overlap method (AOM) The formula (76) may be rewritten in the form... 

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